The original United States Naturalization Law of March 26, 1790 (1 Stat. 103) provided the first rules to be followed by the United States in the granting of national citizenship. This law limited naturalization to immigrants who were "free white persons" of "good moral character". It thus left out indentured servants, slaves, free blacks, and later Asians. While women were included in the act, the right of citizenship did "not descend to persons whose fathers have never been resident in the United States...." Citizenship was inherited exclusively through the father. This was the only statute that ever purported to grant the status of natural born citizen.[1][2]
The 1790 law did not prohibit immigration of the groups listed, only their naturalization as citizens.
It wasn’t until 1875 that immigration of even convicts was prohibited.